If you need assistance with the Subtraction of Rational Numbers then take the help of this article. Check out the steps you need to follow while Subtracting Rational Numbers be them with the Same or Different Denominator. Let us consider a/b, c/d to be two rational numbers then subtracting c/d from a/b is adding the additive inverse of c/d to the rational number a/b.
We can denote the Subtraction of c/d from a/b as a/b – c/d.
Thus we have, a/b – c/d = a/b+(-c/d)[since -c/d is the additive inverse of c/d]
How to Subtract Rational Numbers?
The Procedure to Subtract Rational Numbers having Same and Different Denominators is better explained in the coming modules by considering a few examples. Have a glance at them and solve the Subtraction of Rational Numbers Problems you encounter easily.
Examples
1. Subtract 2/3 from 4/5?
Solution:
Subtracting 4/5 from 2/3
= 4/5-2/3
= 4/5+(-2/3)
= 4*3/5*3+(-2*5/3*5)
= 12/15+(-10/15)
= (12-10)/15
= 2/15
Therefore, 4/5 -2/3 = 2/15.
2. Subtract 3/9 from 2/5?
Solution:
Subtracting 2/5 from 3/9 we get
= 3/9 -2/5
= 3/9+(-2/5)
= 3*5/9*5+(-2*9/5*9)
= 15/45+(-18/45)
= -3/45
= -1/15
Therefore, 2/5-3/9 = -1/15
3. Simplify -6/7-5/8?
Solution:
Given Expression is -6/7-5/8
= -6/7+(-5/8)
= -6*8/7*8+(-5*7/8*7)
= -48/56+(-35/56)
= (-48-35)/56
= -83/56
Therefore, -6/7-5/8 = -83/56
4. What should be subtracted from 4/5 to get the Rational Number 6/15?
Solution:
Let the number to be subtracted as x
From the given data we can write the equation as 4/5-x = 6/15
Rearranging the equation to get the variable x aside we have
4/5-6/15=x
4*3/5*3-6*1/15*1 = x
x= 12/15-6/15
=6/15
The Number to be Subtracted from 4/5 to obtain 6/15 is 6/15.
5. What is the Rational Number to be Added to -7/10 to get 4/7?
Solution:
Let us consider the number to be added as x which results in 4/7
-7/10+x= 4/7
-7/10-4/7 =x
x =-7/10-4/7
= -7*7/10*7-4*10/7*10
= -49/70-40/70
= (-49-40)/70
= -89/70.
Therefore -89/70 when added to -7/10 results in 4/7
6. Sum of Two Rational Numbers is 5/3 if One of the Numbers is 9/20 find the Other?
Solution:
Sum of two rational numbers = One Number + Other Number
5/3 = 9/20+Other Number
Other Number = 5/3-9/20
= 5*20/3*20 – 9*3/20*3
= 100/60-27/60
= 73/60
Therefore, the Other Number to be added to 9/20 to get the sum 5/3 is 73/60.